3h^2+2h-48=0

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Solution for 3h^2+2h-48=0 equation: 


Simplifying
3h2 + 2h + -48 = 0

Reorder the terms:
-48 + 2h + 3h2 = 0

Solving
-48 + 2h + 3h2 = 0

Solving for variable 'h'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-16 + 0.6666666667h + h2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.6666666667h + 16 + h2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.6666666667h + h2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.6666666667h + h2 = 0 + 16
0.6666666667h + h2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.6666666667h + h2 = 16

The h term is 0.6666666667h.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667h + 0.1111111112 + h2 = 16 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667h + h2 = 16 + 0.1111111112

Combine like terms: 16 + 0.1111111112 = 16.1111111112
0.1111111112 + 0.6666666667h + h2 = 16.1111111112

Factor a perfect square on the left side:
(h + 0.3333333334)(h + 0.3333333334) = 16.1111111112

Calculate the square root of the right side: 4.01386486

Break this problem into two subproblems by setting 
(h + 0.3333333334) equal to 4.01386486 and -4.01386486.


Subproblem 1
h + 0.3333333334 = 4.01386486

Simplifying
h + 0.3333333334 = 4.01386486

Reorder the terms:
0.3333333334 + h = 4.01386486

Solving
0.3333333334 + h = 4.01386486

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + h = 4.01386486 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + h = 4.01386486 + -0.3333333334
h = 4.01386486 + -0.3333333334

Combine like terms: 4.01386486 + -0.3333333334 = 3.6805315266
h = 3.6805315266

Simplifying
h = 3.6805315266


Subproblem 2
h + 0.3333333334 = -4.01386486

Simplifying
h + 0.3333333334 = -4.01386486

Reorder the terms:
0.3333333334 + h = -4.01386486

Solving
0.3333333334 + h = -4.01386486

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + h = -4.01386486 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + h = -4.01386486 + -0.3333333334
h = -4.01386486 + -0.3333333334

Combine like terms: -4.01386486 + -0.3333333334 = -4.3471981934
h = -4.3471981934

Simplifying
h = -4.3471981934


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.6805315266, -4.3471981934}

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